Israeli Prime Minister Naftali Bennett has tested positive for COVID-19 but feels well and will work while self-isolating at home, his office said on Monday.

The news came hours after Bennett, who has been vaccinated against the coronavirus and received a booster dose, visited the scene of a shooting in the Israeli city of Hadera, where two Arab gunmen killed two police officers before being shot dead.

"This morning, the prime minister will conduct an assessment ... of last night's attack," Bennett's office added in a statement.

US Secretary of State Anthony Blinken will test for COVID-19 on Monday after having met Bennett in Jerusalem the previous day, a State Department spokesperson said.

"Upon learning of Prime Minister Bennett's positive test result, we determined that only Secretary Blinken is considered a close contact. He will follow all CDC guidance, including by masking and undergoing appropriate testing," spokesperson Ned Price said.

Bennet is in Israel for a two-day visit to attend a landmark meeting with allied Arab countries and Israel. The United Arab Emirates, Bahrain, Egypt and Morocco, the so-called Abraham Accords counties, and Israel will discuss regional issues and US nuclear talks with Iran.